{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mixtures of Gaussians"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import norm\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A _superposition_ of $K$ gaussian densities is known as a **mixture of Gaussians**. We define the probability of $x$ in a mixture of Gaussians as follows:\n",
    "\n",
    "$$\n",
    "    p(\\mathbf x) = \\sum_{i=1}^K \\pi_k \\mathcal N(\\mathbf x | \\boldsymbol \\mu_k, \\boldsymbol \\Sigma_k)\n",
    "$$\n",
    "\n",
    "* $N(\\mathbf x | \\boldsymbol \\mu_k, \\boldsymbol \\Sigma_k)$ is called a _component_\n",
    "* $\\pi_k$ is called the _mixing coeficient_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-3, 3, 100)\n",
    "mu1, mu2, mu3 = -1.2, 1.2, 0.6\n",
    "sigma1, sigma2, sigma3 = 0.4, 0.4, 1\n",
    "pi1, pi2, pi3 = 0.4, 0.2, 0.3\n",
    "\n",
    "c1 = norm.pdf(x, loc=mu1, scale=sigma1)\n",
    "c2 = norm.pdf(x, loc=mu2, scale=sigma2)\n",
    "c3 = norm.pdf(x, loc=mu3, scale=sigma3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a1bc5ddd8>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(16, 5))\n",
    "\n",
    "ax[0].plot(x, c1, label=\"c1\")\n",
    "ax[0].plot(x, c2, label=\"c2\")\n",
    "ax[0].plot(x, c3, label=\"c3\")\n",
    "ax[1].plot(x, pi1 * c1 + pi2 * c2 + pi3 * c3)\n",
    "ax[1].set_title(\"GMM\")\n",
    "\n",
    "ax[0].legend()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
